REFINANCE A SECOND MORTGAGE - DIY MONTHLY PAYMENT CALCULATION

You are watching the Sunday afternoon game and you see an ad from a local mortgage finance company offering 6% second home mortgage financing. You got your current $50,000 second mortgage 5 years ago at 8%. It is a 20 year loan. Is it worth checking out the home mortgage finance company's offer to refinance the remaining balance of your 2nd mortgage for the remaining 15 years at a lower monthly payment? You can get free actual second mortgage refinance quotes here. Let's do the math without leaving the couch.

What can you do to figure out a monthly home loan payment amount if your favorite place to noodle has no computer or internet?. And you have finally lost or tossed out that old HP12c you had in your top drawer since 1992.

The monthly home mortgage payment formula is simple enough but unless you can do logarithms in your head you need a calculator with a power function key. That's the key with y^x (superscript x) on it. For example 2 raised to the 3 power = 8, or 2 x 2 x 2 = 8. On the calculator you would enter 2. then y^x. then 3. then = to get the answer 8. If you have kids in school you probably have a calculator with a power function key lying around the house. Some cell phone calculators will do the trick also.

A compound interest payment calculation is not rocket science but it is not trivial either. Hence the need for a calculator with a power function key. If you do the monthly loan payment calculation half a dozen times you can probably commit it to memory. Worst case is the formula will fit on a small index card that you can slip into your briefcase or purse.

The variables are:
N = mortgage loan period in months. i.e. 15 years = 180 months.
R = mortgage interest rate in whole numbers. i.e. 6% written as 6.
P = principal amount of the mortgage loan. The amount borrowed.
Q = the Q factor. An intermediate calculation.
M = monthly home mortgage payment amount

Here's the entire formula for the monthly payment amount of a compound interest loan:

M = (P * R* Q) / (1200 * (Q -1))

Easy enough, but first you have to calculate the intermediate value of Q. Here is the formula:

Q = (1 + R/1200) ^N

Pretty simple, but you do need the power function key. N can get fairly large.

The current monthly payment on your hypothetical second mortgage is $418.22. The pay-off on the remaining balance of the second mortgage loan at the end of the 60th month is about $43,763. You can see how to do the amortized second mortgage pay off calculations here.

The home mortgage finance company is offering 6% on $43,763 for 15 years. If you decided to refinance your second mortgage what is the monthly payment amount?

Q = (1 + 6/1200) ^180 = 2.454 (intermediate step)

M = (43763 * 6 * 2.454) / (1200 * (2.454 -1)) = $369 (monthly payment).

In this example by refinancing your second mortgage at the lower rate you would pay off your current second mortgage at the same time and have almost $49 more cash per month in your pocket. Let's see. If you invested that $49 per month at a 20% annual return...

What is the current rate to refinance a second mortgage?